Question

Q 1(a) Suppose that all of the matter in the universe were converted into energy in the form of blackbody radiation. Take the average density of matter to be $\rho_{b,0} = 4.17 \times 10^{-28} kg/m^3$ Find the temperature of the Universe in this situation. Using Wien's law ($\lambda_{max} T = 0.0029 mK$) find at what wavelength would the blackbody spectrum peak. Explain how your result may be applied to Olber's paradox.

          Q 1(a)
Suppose that all of the matter in the universe were converted into energy in the form
of blackbody radiation. Take the average density of matter to be $\rho_{b,0} = 4.17 \times 10^{-28} kg/m^3$
Find the temperature of the Universe in this situation. Using Wien's law
($\lambda_{max} T = 0.0029 mK$) find at what wavelength would the blackbody spectrum peak.
Explain how your result may be applied to Olber's paradox.

Q 1(a)
Suppose that all of the matter in the universe were converted into energy in the form
of blackbody radiation. Take the average density of matter to be ρb,0 = 4.17 × 10^-28 kg/m^3
Find the temperature of the Universe in this situation. Using Wien's law
(λmax T = 0.0029 mK) find at what wavelength would the blackbody spectrum peak.
Explain how your result may be applied to Olber's paradox.

Added by Nicholas W.

An Introduction to Modern Astrophysics

Bradley W. Carroll, Dale A. Ostlie 2nd Edition

Chapter 29

Instant Answer

Solved by Expert Kirsty Gledhill

Step 1

If all mass is converted to radiation, energy density u = rho c^2. For blackbody radiation u = a T^4, where a = 7.5657e-16 J m^-3 K^-4 (radiation constant). Use rho = 4.17e-28 kg m^-3 and c = 2.998e8 m s^-1. Wien’s constant b ≈ 2.898e-3 m·K so lambda_max = b / T. Show more…

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Q1(a) [6] Suppose that all of the matter in the universe were converted into energy in the form of blackbody radiation. Take the average density of matter to be Po = 4.17x10^-28 kg/m^3. Find the temperature of the Universe in this situation. Using Wien's law AmaxT = 0.0029 mK, find at what wavelength would the blackbody spectrum peak. Explain how your result may be applied to Olber's paradox.